Solve the following equation with a rational exponent: 5x^4/3=80.(1 point)

To solve the equation \( 5x^{4/3} = 80 \), we can start by isolating \( x^{4/3} \).

1. **Divide both sides by 5**:
\[
x^{4/3} = \frac{80}{5}
\]
\[
x^{4/3} = 16
\]

2. **Now, raise both sides to the power of \( \frac{3}{4} \)** to solve for \( x \):
\[
x = 16^{3/4}
\]

3. **Calculate \( 16^{3/4} \)**:
- First, determine \( 16^{1/4} \):
\[
16^{1/4} = 2 \quad \text{(since \( 16 = 2^4 \))}
\]
- Now raise \( 2 \) to the power of \( 3 \):
\[
16^{3/4} = (16^{1/4})^3 = 2^3 = 8
\]

Thus, the solution to the equation is:
\[
\boxed{8}
\]

So B?

Yes, that's correct! The solution to the equation \( 5x^{4/3} = 80 \) is \( x = 8 \). So the correct response is indeed:

**B) 8**.